Right turn signal stays on will not flash left works.2001 jimmy

make left turns only?

Check the trailer wires for damaged wires that may be crossing.

Sounds like the turn signal switch is bad, since the brake light circuit is routed through the turn switch.

lol sounds like my old truck most likely crossed wires

My first guess would be a ground problem. The bulbs are mounted in plastic sockets and grounded to the car by a black wire. If one socket is not grounded it will try to ground thru a different socket.
I would check for voltage and ground on each socket in the back.

Standard wiring colors are as follows:

4-Way

5-Way

6-Way

7-Way

Green

Yellow

Brown

White

Red

Blue

Purple

Right Turn & Brake

Left Turn & Brake

Tail Lights

Ground

Backup Lights

Electric Brakes

Auxiliary Power
Green- Right Turn and Brake
Yellow- Left Turn and Brake
Brown- Tail Lights
White- Ground
Red- Reverse (Back Up) Lights
Blue- Electric Brakes
Purple- Auxiliary Power

It sounds like your green and yello wires are shorted together somewhere along the length of the harness. I would check the wires on the trailer first. Easier yet, if you have another trailer to connec or access to another to use for testing, connect to it and see if the problem repeats; if it does the trouble is in the vehicle's wiring.

you need to replace the flasher unit

Flasher Unit sounds bad... change the flasher, which is in the inboard fuse panel.

Rear lights are double filament bulbs one side for the lights other side for the brake/turn signals so it still may be a bulb. Do u have a test light or volt meter you can check to make sure u have power there when brakes or turn signals are activated. Or just try another bulb.

check the rear bulbs

I had the same problem with my 2001. I found it was the multi function switch. Better known as your turn signal switch. I found that the hazard switch portion of it had shorted. replacement is fairly easy, aftermarket part is available, much cheaper than GM.